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amelapal Group Title

4 sin^4 x + 3sin^2 x - 1 = 0 After I borrow the 4 I just don't know what to do afterwords..

  • one year ago
  • one year ago

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  1. Iamgmg90 Group Title
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    let sin^2x = u, substitute and solve as a quadratic? i.e 4u^2 + 3u - 1 = (4u - 1)(u + 1 ) so u = 1/4 or -1, therefore sin^2(x) = 1/4 or -1, use calculator

    • one year ago
  2. Iamgmg90 Group Title
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    sin^-1(SQRT(1/4) = sin^-1(1/2)

    • one year ago
  3. amelapal Group Title
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    Can the quadratic formula be used if its to the 4th degree because I got the same thing, however I used factoring with borrow and payback.

    • one year ago
  4. ByteMe Group Title
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    Yes... you can use the QF but I think factoring, as shown above is faster...

    • one year ago
  5. ByteMe Group Title
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    Also, \(\large sin^2x=\frac{1}{4} \) gives \(\large sinx=\pm \frac{1}{2} \) so you'll need to solve sinx=1/2, and also sinx=-1/2

    • one year ago
  6. Iamgmg90 Group Title
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    Oh, thanks. Yes square rooting yields both signs, as squaring makes positive (negative time negative). The -1 can be ignored as it would be a complex number

    • one year ago
  7. ByteMe Group Title
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    yep...

    • one year ago
  8. amelapal Group Title
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    So the angles would be 30 and 150, and 210 and 330?

    • one year ago
  9. amelapal Group Title
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    The other one would come up with i so is it okay to ignore it since it is complex?

    • one year ago
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